Knowing that the tension in wire BD is 650 N, determine the reaction at the fixed support C of the member shown. You must include FBD. 750 N 150 mm 250 mm -500 mm 400 N m 450 N 600 mm 400 mm

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Problem Statement:**

Knowing that the tension in wire BD is 650 N, determine the reaction at the fixed support C of the member shown. You must include the Free Body Diagram (FBD).

**Diagram Description:**

The diagram illustrates a structural member with various forces acting on it, depicted as follows:

1. **Dimensions and Structure:**
   - The member starts vertically at point C and extends horizontally to the right for 400 mm.
   - It then bends 90 degrees upward at point A and continues vertically upwards for 500 mm.
   - Another horizontal segment extends to the right from point B for 250 mm. Point B is 150 mm above point A.

2. **Applied Forces:**
   - A force of 750 N is acting vertically downward at point B.
   - A force of 450 N is acting horizontally to the right at point D, which is 600 mm below point B and to the right of C.
   - A moment of 400 N·m is acting counter-clockwise at point A.

3. **Supports:**
   - The member is fixed at point C, which means it can resist horizontal and vertical forces as well as a moment.
   - Wire BD is supporting the member, creating a tension of 650 N in the wire.

**Free Body Diagram (FBD):**

In a Free Body Diagram, you need to illustrate all forces acting on the isolated member, including reactions at supports and external forces. For this member, the FBD should include:

   - Reaction forces at the fixed support C: 
     - \( C_x \): horizontal reaction force.
     - \( C_y \): vertical reaction force.
     - \( M_C \): moment reaction.
   
   - External forces and moments:
     - 750 N downward force at point B.
     - 450 N rightward force at point D.
     - 400 N·m counter-clockwise moment at point A.
   
   - Tension in the wire BD (650 N).

The FBD is essential for setting up equilibrium equations to solve for the unknown reactions at support C.

**Steps to Solve:**

1. **Draw the FBD:**
   - Indicate all external forces, moments, and support reactions.
   - Represent the tension in wire BD, breaking it into its horizontal and vertical components, if necessary.

2. **Set Up Equilibrium Equations:**
   - Sum of Forces in the
Transcribed Image Text:**Problem Statement:** Knowing that the tension in wire BD is 650 N, determine the reaction at the fixed support C of the member shown. You must include the Free Body Diagram (FBD). **Diagram Description:** The diagram illustrates a structural member with various forces acting on it, depicted as follows: 1. **Dimensions and Structure:** - The member starts vertically at point C and extends horizontally to the right for 400 mm. - It then bends 90 degrees upward at point A and continues vertically upwards for 500 mm. - Another horizontal segment extends to the right from point B for 250 mm. Point B is 150 mm above point A. 2. **Applied Forces:** - A force of 750 N is acting vertically downward at point B. - A force of 450 N is acting horizontally to the right at point D, which is 600 mm below point B and to the right of C. - A moment of 400 N·m is acting counter-clockwise at point A. 3. **Supports:** - The member is fixed at point C, which means it can resist horizontal and vertical forces as well as a moment. - Wire BD is supporting the member, creating a tension of 650 N in the wire. **Free Body Diagram (FBD):** In a Free Body Diagram, you need to illustrate all forces acting on the isolated member, including reactions at supports and external forces. For this member, the FBD should include: - Reaction forces at the fixed support C: - \( C_x \): horizontal reaction force. - \( C_y \): vertical reaction force. - \( M_C \): moment reaction. - External forces and moments: - 750 N downward force at point B. - 450 N rightward force at point D. - 400 N·m counter-clockwise moment at point A. - Tension in the wire BD (650 N). The FBD is essential for setting up equilibrium equations to solve for the unknown reactions at support C. **Steps to Solve:** 1. **Draw the FBD:** - Indicate all external forces, moments, and support reactions. - Represent the tension in wire BD, breaking it into its horizontal and vertical components, if necessary. 2. **Set Up Equilibrium Equations:** - Sum of Forces in the
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